Group action invariants
| Degree $n$ : | $16$ | |
| Transitive number $t$ : | $1174$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $4$ | |
| Generators: | (1,11)(2,12)(3,10)(4,9)(5,15,8,13)(6,16,7,14), (1,15,3,14)(2,16,4,13)(5,8)(6,7)(9,10)(11,12), (1,3)(2,4)(5,9,8,11)(6,10,7,12)(13,15)(14,16) | |
| $|\Aut(F/K)|$: | $4$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 7 4: $C_4$ x 4, $C_2^2$ x 7 8: $D_{4}$ x 12, $C_4\times C_2$ x 6, $C_2^3$ 16: $D_4\times C_2$ x 6, $C_2^2:C_4$ x 12, $C_4\times C_2^2$ 32: $C_2^2 \wr C_2$ x 4, $C_2^3 : C_4 $ x 4, $C_2 \times (C_2^2:C_4)$ x 3 64: $((C_8 : C_2):C_2):C_2$ x 4, $(((C_4 \times C_2): C_2):C_2):C_2$ x 2, 16T76 x 2, 16T79, 16T146 x 2 128: $C_2 \wr C_2\wr C_2$ x 4, 16T227 x 2, 16T240, 32T1151 x 2 256: 16T482 x 2, 16T502, 16T532, 16T542 x 2, 16T543 512: 32T12349 x 2, 32T13346 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 4: $D_{4}$
Degree 8: $(((C_4 \times C_2): C_2):C_2):C_2$, $C_2 \wr C_2\wr C_2$ x 2
Low degree siblings
16T1174 x 127, 32T36002 x 32, 32T36003 x 64, 32T36004 x 32, 32T36005 x 64, 32T36006 x 32, 32T36007 x 64, 32T36008 x 32, 32T36009 x 64, 32T36010 x 32, 32T36011 x 32, 32T36012 x 32, 32T44990 x 16, 32T44991 x 16, 32T45009 x 32, 32T46587 x 16, 32T48995 x 16, 32T48997 x 16, 32T49071 x 32, 32T50170 x 32, 32T50733 x 32, 32T50792 x 32, 32T52298 x 16, 32T52316 x 32, 32T54908 x 16, 32T54918 x 32Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 70 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $1024=2^{10}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |